Question

AB and BC form a right angle at point B. If A = (-3, -1) and B = (4, 4), what is the equation of BC?
x + 3y = 16
2x + y = 12
-7x − 5y = -48
7x − 5y = 48

Answer 1

@Michele_Laino

Answer 2

@AdoNine

Answer 3

here, we have to write the equation of line AB first

Answer 4

yes

Answer 5

the slope \(m\) of such line is:
\[m = \frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} = \frac{{ - 1 - 4}}{{ - 3 - 4}} = ...?\]

Answer 6

5/7?

Answer 7

Would the answer be 7x − 5y = 48 ?

Answer 8

correct!
I think it is suffice so
since line BC is perpendicular to line AB, then its slope \(m'\) has to check this identity:
\(m \cdot m'=-1\)
namely:
\[m' = \frac{{ - 1}}{m} = \frac{{ - 1}}{{5/7}} = ...?\]

Answer 9

@austinlr12 you are correct

Answer 10

Thxs

Answer 11

Please wait, I'm checking...
and the requested equation, is therefore:
\[y - 5 = \frac{{ - 7}}{5}\left( {x - 5} \right)\]

Answer 12

oops.. I have made a typo:
\[y - 4 = \frac{{ - 7}}{5}\left( {x - 4} \right)\]

Answer 13

I got this equation:
\[7x + 5y = 48\]

Answer 14

I already submit the answer...